Which Annuity Formula to Use for Birthday Deposits?

[gillgill]

A father opened a savings account for his daughter on the day she was born, depositing $1000. Each year on her birthday he deposits another $1000, making the last deposit on her twenty-first birthday. If the account pays 9.5% interest compounded annually, how much is in the account at the end of the day on the daughter's twenty first birthday?

For this question, which formula do i use?
ordinary annuity: where payments are made at end of time period
or
annuities due: where payments are made at beginning of time period
?

 

[Tide]

You use the simple equation for compound interest and apply it to each deposit made over the course of 21 years --- and then add them all up. :)

 

[gillgill]

but this section is about annuity...ordinary annuity and annuities due are the two equations. Out of these two, which one should i use?

 

[Tide]

Tell us how your textbook defines those terms! :)

 

[gillgill]

ordinary annuities: those with payments made at the end of each time period.

annuities due: annuities in which payments are made at the beginning of each time period.

 

[Tide]

Good. And the father is making payments at the beginning of each compounding period ... therefore ...? :)

 

[HallsofIvy]

Most mathematicians don't have "annuity" formulas at their fingertips but here I responded to a similar question working out the formula as Tide suggested:
https://www.physicsforums.com/showthread.php?t=101617

 

[gillgill]

okay...so i use the annuity due formula...
thx.